The on-line advertising market has become a principal source of revenue for search engine companies. The business model relies on advertisement sales that provide advertisers with opportunities to introduce their products directly to potential customers. The business model, known as sponsored keyword auction, identifies each user of a search engine, who submits a keyword or several keywords to the search engine, as a potential customer to related consumer products. Web links displaying those products are listed along with the search results of the queried keywords. To win the slots for displaying positions of web links, advertisers compete through an auction process.
Some advertising positions draw more attentions from users and generate more clicks than others. Therefore, different advertising positions have different click-through-rates, the ratio of the number of clicks on the advertising to the number of appearances of the advertising web links. For this reason, it is named the position auction or Generalized Second Price (GSP) auction.
Conventional researches model the position auction together with the bidding strategies of advertisers (or agents) as a pure Nash equilibrium, in which an agent will choose a strategy that maximizes the agent's own utility with respect to a given set of strategies of other players. However, in a pure Nash equilibrium, optimal agent utility is not maximized since bidders of a pure Nash equilibrium do not consider the influence their bids have on future decisions of other bidders—the pure Nash equilibrium does not consider the indirect influence bids have on others' future bidding decisions.
It is therefore desirable to have systems and methods for improving social efficiency, and improving the revenues of all the auctioneers and bidder.